Question

If you know the $\left[{\mathrm{OH}}^{-}\right]$, how can you determine the pH of a solution?

Short answer

The pH of a solution is determined as $pH=-\log \left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]$

Step-by-step solution

Introduction 

The objective is to determine the pH of a solution when $\left[{\mathrm{OH}}^{-}\right]$is known.

Explanation 

We'll start by calculating the ${\mathrm{H}}_3{\mathrm{O}}^{+}$using $K_{\omega }$(Ionic product) for water i.e localid="1653974998099" $K_{\omega }=\left[{\mathrm{H}}_3^{+}\mathrm{O}\right]\times \left[{\mathrm{OH}}^{-}\right]$and $\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]=\frac{{\mathrm{K}}_{\omega }}{\left[{\mathrm{OH}}^{-}\right]}=\frac{1.0\times {10}^{-14}}{\left[{\mathrm{OH}}^{-}\right]}$

Then enter the calculate value $\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]$far computation based on formula$\mathrm{pH}$, which is

localid="1653975011962" $\mathrm{pH}=-\log \left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]$

As a result, pH can be determined